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Math Help - Another really neat theorem!

  1. #1
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    Another really neat theorem!

    This is not for help or anything; just a neat factoid. The number of odd numbers in the nth row of pascal's triangle is 2^k, where k is the the number of ones occuring in the binary representation of n.
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  2. #2
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    The generalization of this theorem is that if  n = a_m a_{m-1}... a_0 the representation of  n in base prime  p , then the number of the binomial coefficients which are prime to p is  (a_0 + 1 )(a_1 + 1 )...(a_m + 1 ) .
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